Uniform rectilinear motion
An airport moving walkway. A train on a straight track that neither brakes nor speeds up. Both move in a straight line and always at the same speed. That has a name: URM.
What URM is
We drop a bead of dye into a test tube of glycerine: every second it sinks exactly $4\ \text{cm}$ in a straight vertical line. How can we relate position and time mathematically for an object that never changes its pace?
An airport moving walkway moves in a straight line and always advances at the same speed. a) What type of motion does it describe? b) State the two conditions that…
An airport moving walkway moves in a straight line and always advances at the same speed.
- a) What type of motion does it describe?
- b) State the two conditions that motion must satisfy to be uniform and linear.
The position equation
Move the sliders for $x_0$ and $v$. The graph of $x(t)$ and the equation above change with your values.
A pedestrian moves with uniform linear motion according to the equation $x = x_0 + v \cdot t$, with $x_0 = 10\ \text{m}$ and $v = 2\ \text{m/s}$. Calculate their…
A pedestrian moves with uniform linear motion according to the equation $x = x_0 + v \cdot t$, with $x_0 = 10\ \text{m}$ and $v = 2\ \text{m/s}$. Calculate their position when $t = 5\ \text{s}$.
The position of a scooter, in International System units, is $x = 50 - 4 \cdot t$. a) Explain what the minus sign on the velocity means: is it moving away from or…
The position of a scooter, in International System units, is $x = 50 - 4 \cdot t$.
- a) Explain what the minus sign on the velocity means: is it moving away from or towards the origin?
- b) Calculate its position when $t = 5\ \text{s}$.
A runner maintains a constant speed of $18\ \text{km/h}$. a) Express their speed in $\text{m/s}$. b) How long does it take them to cover $200\ \text{m}$?
A runner maintains a constant speed of $18\ \text{km/h}$.
- a) Express their speed in $\text{m/s}$.
- b) How long does it take them to cover $200\ \text{m}$?
Changing units: km/h and m/s
A train passes through a station without stopping, at $108\ \text{km/h}$, and maintains that speed. We take the station as the origin. a) Express the speed in…
A train passes through a station without stopping, at $108\ \text{km/h}$, and maintains that speed. We take the station as the origin.
- a) Express the speed in $\text{m/s}$.
- b) Write the equation for its position.
- c) Calculate its position $45\ \text{s}$ after passing through the station.
A toy car moves according to the equation $x = 200 - 10 \cdot t$, in International System units. a) At what instant does it reach the origin? b) What is its position…
A toy car moves according to the equation $x = 200 - 10 \cdot t$, in International System units.
- a) At what instant does it reach the origin?
- b) What is its position when $t = 12\ \text{s}$?
Meetings between two moving objects
Two skaters $300\ \text{m}$ apart set off at the same time towards each other along a straight track with constant but different velocities: at exactly what point on the track will they cross, and how long will it take them to meet?
Two cities are connected by a straight railway line of $300\ \text{km}$. A train leaves city A for B at $90\ \text{km/h}$ and, at the same time, another leaves city B…
Two cities are connected by a straight railway line of $300\ \text{km}$. A train leaves city A for B at $90\ \text{km/h}$ and, at the same time, another leaves city B for A at $60\ \text{km/h}$. The situation is shown in the figure.
- a) How many kilometres do they get closer to each other every hour?
- b) How long do they take to cross paths?
- c) At what distance from city A do they cross paths?
A cyclist leaves a point at $6\ \text{m/s}$. Ten seconds later, a scooter leaves from the same point in the same direction at $10\ \text{m/s}$. a) Write the position…
A cyclist leaves a point at $6\ \text{m/s}$. Ten seconds later, a scooter leaves from the same point in the same direction at $10\ \text{m/s}$.
- a) Write the position equation for each vehicle taking $t = 0$ when the scooter starts. Remember that when the scooter starts, the cyclist already has a $10\ \text{s}$ head start.
- b) How long does it take for the scooter to catch up with the cyclist?
- c) At what distance from the starting point does it catch up?